Greedy Goblin

Wednesday, January 20, 2010

Glass ceiling

Another completely non-WoW post, skip it. There is a normal post today.

As I wrote once (and had a 50+ comment + mail scientific debate with Phaelia), my "hobby" back at PHD course was evolutionary biology. I wanted to find out why higher class animals have two sexes instead of being hermaphrodites like plants. I found a very interesting dataset, but since I couldn't include it into the theory, I've put it into a folder. Now I found further research data to use it.PISA is an official OECD programme to check if school students are "well prepared for future challenges? Can they analyse, reason and communicate effectively? Do they have the capacity to continue learning throughout life?" I've downloaded the whole detailed dataset. (beware, 750MB and need statistical software to read)

No, I don't want to point out that girls performed worse in mathematics and natural sciences. The feminists are right that this is completely the effect of the society that drives girls towards humanities, where they outperform the boys. This could and should be fixed by proper education. What I found is that in every field the results of boys had 5% more standard deviation than the girls. This 5% was extremely rigid and invariant to field, age and the average score.

To understand what standard deviation is, look at the picture below, where the green line has 100% more standard deviation.Their average is equal. The amount of "greens" who are better than 0 is exactly 50%. The amount of "reds" who are better than 0 is exactly 50%. Yet the amount of "greens" who are better than 2 are visibly larger than "reds". Also the amount of "greens" who are worse than -2 is visibly larger than reds.

Of course 5% is little, so the effect is much less visible. But let's make a calculation. Let's assume that an average woman is just as smart as an average man. Let's also assume, that the average "smartness" of people is 100, the standard deviation is 15. If you have deja vu, it's not a mistake. I also assume that half of the population is female.

The 5% means that the standard deviation for women is 14.63, while it's 15.37 for man. The following chart shows woman:men ratios in top groups:

top 50%: 1.00, meaning that exactly as many women are above average than men

top 10%: 0.90

top 1%: 0.74

top 0.1%: 0.60

top 0.01%: 0.48

top 0.001%: 0.39

top 0.0001%: 0.31

This explains the "glass ceiling" effect, why there are few women in top jobs. Simply, among the people who are capable of being in the very top, there are less women. Of course this has an opposite effect, men overpopulate the bottoms too. There are much more men in prison, mental hospital or homeless shelter than women. Men are not better in general, they just have more extremes in both good and bad ways. This obviously means that the feminist attempts to enforce 50% female ratio in politics or CEO levels are futile.

Note: I found this strange effect alone, but I obviously don't claim that I was the first to find it. I simply don't know the literature enough to find proper links.

------------------- Second part with more science --------------------

The new results that made me pick this post out of the file support the theory, that the male Y chromosome, despite considered being small, fragile and weak, is enduring and stable, due to having the important genes as duplicates on itself.

Why is it important? Because the previously believed slow decay of Y was a major hole in my other theory that explained the dominance of split-sex multiplication over hermaphrodity. The central point of the idea is the bigger variance of males due to their XY chromosome. The reason for increased variance is simple. In case of a single-gene property, the female can have: AA, aa, Aa, aA genom, while males can have AY and aY only:

If we assign "1" phenotype to the AA (or AY) genotype "0" to aa (or aY) and 0.5 to Aa, both sexes has 0.5 average. However the standard deviation for males is 0.5, while only 0.35 for females. Aa is usually not completely in the middle of AA and aa, in extreme dominant-recessive case it's 1 or 0. However, in these extreme cases the female standard deviation is 0.43 while male is still 0.5.

The point of this natural phenomenon is using the males as "probes" while keeping the females safe. Since the parents of the generation were capable of having offspring, we can assume that the "average" offspring is also capable. Offsprings far from the average can be more successful than the "average", or - usually - less successful. The low female variation means that females, who are close to the average, similarly to their parents will survive and have offspring. If a new gene gets into the female, she will be heterozygote (Aa), so the effect of the new gene will be decreased by its counterpart.

The high male variation means that there will be very different males. If a new gene gets into a male, it will show its full effect. If it works, the carrier male will spread it. If it doesn't, he will die and kills the bad gene.

26 comments:

if you didn't know this was stated by the the president of Harvard University, he was flamed to death

"It does appear that on many, many different human attributes-height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability-there is relatively clear evidence that whatever the difference in means-which can be debated-there is a difference in the standard deviation, and variability of a male and a female population. And that is true with respect to attributes that are and are not plausibly, culturally determined."

As a molecular geneticist myself, I'd have to disagree with your methodology here.1. There are no consistent numerical representations for phenotypes in which you can do statistical analysis on.2. Even if there is, the frequency of different alleles (A/a) is dynamic and subject to selection factors and drift. (see: population genetics) Here you basically say A and a each appears 50% of the time.3. I'm not sure what you mean by "a new gene gets into a male/female", if you're trying to say random mutation giving rise to a new genotype, see population genetics again.

@Wildhorn: And that's why there is a real post for today. BTW the mentioned rule applies to philosophy posts, and not such extra posts.

@Sager: but he did not published experimental research. Attacking powerful political groups without ammunition is silly. I'd love to see the feminists trying to explain the PISA results.

@Wildhorn: 1: there is, the chance of survival and creating offspring. Of course we don't know this number, but it exists and in the case of non-neutral mutations, these numbers vary by alleles2: 50% is an example. At ANY "A" percentage the XY (or to be very accurate X0) male has higher fenotypical variance than the female. For example with 90% "A" the males have 90% AY, 10% aY, variance=0.3. Females have 81% AA, 0.18Aa, 0.01aa; variance=0.21 in case of perfect intermedier phenotype, 0.1 in case of perfect A dominance.3: more accurately "if a new mutation happens, or a rare allele is inherited"

If for arguments sake you accurately conclude that the PISA results show that there is a greater range of intelligence with men i cannot see how it can necessarily follow that this is why men have higher tier jobs.

I think the abundance of men in top paid jobs is determined by social factors which are not limited to, but are nonetheless affected by their ability to bear children and how that takes them away from work.

Something which may or may not be of interest is something i read in New Scientist a very long time ago (i cannot find source unfortunately). There was an article talking about the pay in the science industry and difference between the salaries for men and women. Once conclusion that was drawn is that women were more likely to take jobs with static reliable pay and men were more likely to take a lower pay that had added performance based benefits.

What the gender ratio is in such jobs i don't know.

Neither do i know whether the female choice to avoid risk with rewards is a social or biological response.

oops deleted a sentence from my previous post in draft and put one in that doesnt make sense.

I think the abundance of men in top paid jobs is determined by social factors which are not limited to, but are nonetheless affected by their ability to bear children and how that takes them away from work.

Should read:

I think the abundance of men in top paid jobs is determined by social factors which are not limited to, but are nonetheless affected by the ability of a woman to bear children and how that takes them away from work

But In fact, most genes are present on the other 22 pairs of chromosomes. These chromosomes are linked independently of the sexual chromosomes and can manifest themselves in both males and females. For example, thalassemia.

@Anonymous: I'm fully aware that there are somatic chromosomes, where this does not apply. However the X chromosome has much more genes than an average somatic chromosome, so this effect is not negligable (granted, also not total like in several insects where the male is haploid and the female is diploid)

I want to make sure I'm drawing to the right conclusion here. My eyes began to glaze once you got into the genetics.

The Y chromosone is fragile, which could imply that it is more prone to genetic mutations, while the X chromosone is less prone (I believe I read an article about this once before). This leads to a situation where males are more likely to exhibit new genetic mutations than females. This would be logically desirable for continuation of the species since female humans gestate for nine months.

One of the last things you want is for the creature carrying future generations to be in the midst of genetic experimentation and possibly die, taking a new member as well as continued children away from society.

In other words, males are genetically predisposed for new mutations, thus demonstrated how more men are out at the higher deviations when compared to women.

So that would mean most genes related to IQ, aggressivity and so on are located on the X chromosome in your theory ?

I find that hard to believe, but to further your point none the less see : http://www.nature.com/news/2010/100113/full/463149a.htmlThis shows the rapid changes that appeared between chimps Y chromosome and us. This indicates a very high volatility of this chromosome.

I would prefer an explanation involving transcription factors or epigenetics effects based on the Y chromosome. This would make more sense (although it's more a debate on the cause than on the effect).But this is interesting, even if it is not politically correct ^^

@Gilles: it's not necessary that all or even most of the intelligence-genes are on X. It's enough if some are there. Remember that the intelligence variance-difference is just 5%. But in the long run, 5% is enough.

Well that is some very interesting data. I don't think I've ever heard of a connection like that. In case you were interested I know there was some article on the BBC that talked about other factors that allow for even more mutation in the Y chromosome vs the X. http://www.wi.mit.edu/news/archives/2010/dp_0113.html

Let's assume that there's a gene on the X chromosome with 2 possible alleles A and a, then a female would have possible genotypes of AA, Aa, and aa, and a male AY and aY (or in fact A and a). In this case, males have higher standard deviation in genotype.

However, genotypes and phenotypes rarely have 1-to-1 relationships. Often multiple genotypes manifest the same phenotype. In the simplest case, you have allele A completely dominant over a, so your standard deviation is identical to that of male. (Not sure how you came up with 0.43)

In the less often case of codominance between two alleles, Aa manifests a distinct third phenotype that is inaccessible to males. Now, to claim that Aa should have the average score of AA and aa is ridiculous, because it is entirely possible that this new phenotype is vastly advantageous/lethal compared to the homozygous phenotypes (see: sickle cell anemia). Here you have a case where females have access to the extremes of the spectrum due to higher possibilities of phenotypes, where males do not.

@Lupius: in case of codominance, it CAN happen that Aa's phenotype is not somewhere in the middle of AA's phenotype and aa's. However it's more often is than not. If the gene is one of many defining a multi-genom phenotype like intelligence, then Aa must be in between.

Please also note that in the case of a recessive new mutation, males are the ONLY way for the new allele to show itself, as in females it can be only Aa, and it's supressed (it can't be aa as it's a new mutation, alone in the universe)

Thanks for an interesting post. However, I think some care must be taken in interpreting results like this.

1. Your results alone do not demonstrate that the higher variation amongst males is a result of genetic variation. Whilst this is a plausible explanation, social pressures are also a major factor. To draw the conclusions that you do, you need to demonstrate that social factors are negligible compared to genetic ones. This would be hard to do given subjects that are drawn from human society.

2. Even if this were to be the case, something being natural is not the same thing as something being desirable. One might just as well argue that the genetic differences mean that we should try harder to assist women at the top of society (and men at the bottom, for that matter).

3. You'd need to demonstrate that the skills where women are less prone to exhibit at the highest level are more important to leadership than ones where they are stronger. For example, imagine that it were shown that women have a lower standard deviation in IQ & EQ, but their average EQ is higher. What is the relative importance of social skills in leadership compared to raw intelligence?

4. In real-life politics, complex messages like the one you are trying to communicate here are at risk of being boiled down into simplistic sound-bites, e.g. "There is no discrimination, women just aren't good enough to run big businesses." Now I know that's an oversimplification of what you're trying to say, but when there's only a 30s slot on the news to get a point across, that's what it can get boiled down to.

With all due respect, your view on deviation is rather black and white.

The most dire genetic diseases are not defects in the genome but rather chromosomal anomalies. In fact, most of the diseases that are linked to sterility, mental retardation and so forth, are directly linked with trisomies, or monosomies and not punctiform genic mutations. Let alone the fact that most X-linked diseases are nowhere near fatal and such your claim that males showing those diseases in the phenotype will die. That's a shock-jock statement and you know it. It just scares people (people who are ill-informed about genetic diseases as is). If, for some reason a genic mutation is lethal, it will lead to a stillborn or abortion. No chance in hell that an incompatible mutation makes its way into the gene pool.

I'll go more in-depth about this. Any genic mutation usually occurs when nuclear acids are 'copied' one after another. However there are lots of enzymes that control this process and it's fairly unlikely that such a mutation will occur 'de novo' and not be caught in the act.

The nondisjunction of chromosomes in reproductive cells are far more common and with more severe consequences. The chromosomal cross-over is another error-prone transition.

1. There are at least a few examples where which parent a gene comes from is very important (i.e. Angelman vs. Prader-Willi syndromes are the same abnormality, but it manifests differently depending on which parent it comes from).

2. Most if not of the duplicate X genes are turned off--one X chromosome is silenced in each cell, so women aren't as redundant as you think.

3. In birds and some other stuff, the sex determination is opposite (females are ZW, males are ZZ).

On discrimination vs. innate ability in glass ceilings, I give two examples (and then I am done). First, although professional orchestras INSISTED that they were picking the most deserving musician from open auditions (and that the men were just better), when they went to blind auditions, the % of women moved from practically none to matching the representation in the applicant pool.

Second, a recent (2005ish) study looking at perception of male vs. female scientists looked at this issue (sort of). Publications were numerically scored by impact factor to give a productivity score. Every person in the study was ranked into quartiles. Scientists (male and female) were recruited to rank the CVs based on competence. For both male and female subjects, only women in the top quartile were ranked as competent as the bottom quartile of men. None of the other women were ranked as competent as the men, even though they objectively were. (The study is in Nature, if you have access to a library that gets it).

In both cases, it is unconscious bias, and the effect is much larger than 5%. When we get rid of that, we can worry about the 5% difference in variance.

In your first example you make a large leap in assumptions, that there is a direct correlation between how high your IQ is and how 'high up' your job is. The status/income/responsibility of your job, and the number of females in that job are not always related to IQ - and if you believe they are then you should show HOW.

I was a Life Sciences Major specialising in BioMedical Sciences. Your last portion trying to explain on the variance is a little off the mark.

First of all, you tried to attribute the variance due to the Y chromosome. Since it is shorter, it isn't able to balance out whichever effect is applied by the X chromosome since be it dominant or recessive, it will be expressed.

This would only be valid if all the traits of a male are found solely on the Y chomosome. Which isn't the case. Characteristics inherited from the parents are distributed all over the 23 pairs of chromosomes, hence whichever gene pair effect which is supposed to exibit the variance would be restricted to those found only on the last pair of chromosome.

However, the presence of this difference in X and Y chromosome is attributed to gender linked diseases which were more prone to exhibit its charactistics in male and not females. One such example would be colour blindness. Females seldom have colour blindness as they would require double recessive gene on their XX chromosome to be colour blind. BB - NormalBb - NormalbB - Normalbb - Colour blindThe chances are lower than 25% as you would require both parents to be either carriers or be colour blind positive to even have a chance to be colour blind.

While males, having only 1 single X chromosome would have colour blindness if they get 1 of the recessive genes.BY - NormalbY - Colour blindIf the mum is colour blind, you can be 100% sure the son would be colour blind. However if the mum is just a carrier, the son would have a 50-50 chance. Dad's gene in this case has no effect.

Anyway Lupius is right, what about drift? And the idea that the Y is fragile, I'm not sure where you get that. There are fragile sites in many chromosomes, and the X chrosome even has a disease named after one of these sites.

If you look at the genetics of the Y, there are only a handful of useful genes; and there are only a handful of protein products that cause male determination (which is really really interesting in and of itself). Nonetheless, I just don't see the Y having a bunch of useful genes, it just doesn't.

I did some Y research back in the day, its actually good for studying human populations because of the lack of recombination, like the mtDNA is.

I think everyone is entitled to opinions and theories though. My theory is that we have created social evolution. Men are naturally stronger and more agressive than women. We take the risks, women by and large do not. We do the dangerous jobs, the unpredictable jobs.

My wife had a straight bee-line into her chosen career and now excels at it. I on the other hand have now switched careers because the previous career (biomedical scientist) was too boring for me (not enough risk I guess). Anyway women care most about raising a family. For many men, we could care less about the survival of our offspring. Therein lies the difference. You have to be willing to sacrifice the lifestyle of your offspring to get ahead (turn them into latchkey kids). If you don't want latchkey kids, you simply aren't going to have much of a career. You can choose on or the other. This thought is only related to women (by and large).

Ah, finally I see what you are saying. The genes on the X which aren't present on the Y allow for a certain variability? In that case wouldn't you expect women to have more diversity? Don't forget RL is much more complex than the one gene two allele model.

To me, the idea that women need to be able to take care of their offspring adequatally explains the differences in payscale and so forth.

Anyway I really wouldn't use genetics as a crutch to say you are underperforming. You are underperforming because you are not goblinish enough (you being the hypothetical)

interesting and understandable for layperson explanation. For modern-day comparisons, I've thought that it's just social attitudes. Not everyone would want to be an executive officer in a corporation or government if given the choice.

The book that seems most scientifically correct (but politically incorrect) in this situation would be Hans Eysenck's 'Genius - The natural history of creativity'.

First of all: males have on average a (slightly) higher IQ than females (2-4 points, due to slightly bigger brains). IQ-tests are however designed to eliminate/hide this difference.

Second: yes, males have higher SD.

Third: the curves of IQ are not really Gaussian, more Pearson (type IV, if I recall correctly), so they are wider; which means that a higher SD gets translated into even more genius (and moron) males than you'd expect from a regular Gaussian.

So yes, in the extremely high IQs you'd expect many more males than females.

HOWEVER, IQ does not seem to correlate a lot to RW success (at least, only 4% within a profession). A scientist with an IQ of 130 has about equal chance to win a Nobel prize as someone with 180 IQ. There are some Nobel prize winners known with IQs around 135- not terribly impressive. Above IQ 120-130, it seems that other factors than IQ (such as social skills, ambition) become much more important.

Part of the glass ceiling is indeed through discrimination by males. But part is also that a greater proportion of talented females chooses careers outside (for example) science or business; this may have some evolutionary grounds too. Still, females are individuals, not clones of each other; there is no reason why a female (in a fair world) could not leave all males behind her in her profession/calling (with some exceptions like the 100m sprint, where it would be hard; similarly, the average female can discriminate tastes much better than even the greatest male chief). But intellectually, males and females are so close as to make a negligible difference.